Additionally, to compare the percentage chances of, five or six point Fire Bet, Small All Tall and Three of the same number Hardway (let's say 8 for example) rolling before a Seven. Hope that made sense..It's a tough one..Thanks in advance!

Quote:VegasHardwayFirst, I searched around and I apologize in advance if these question been answered before.. ( I could not find it).. Was trying to find what is the percentage chance of Hard 8 rolling three or four times before a Seven out? Also, it would be nice to know the percentage difference with the hard 8 turned on and off on the come out roll.

Additionally, to compare the percentage chances of, five or six point Fire Bet, Small All Tall and Three of the same number Hardway (let's say 8 for example) rolling before a Seven. Hope that made sense..It's a tough one..Thanks in advance!

1.) Whether or not you have the bet on during a CO roll is immaterial to the probability.

2.) There are six ways to roll a Seven and one way to roll a Hard Eight, thus, the probability of one Hard Eight before a Seven is 1/7. However, it is important to remember that Soft Eights also cause a Hard Eight to lose, and there are four ways to roll those. Therefore, the probability of rolling a winning Hard Eight is 1/11.

Two Hard Eights w/o Loss: (1/11)^2 = 0.0082644628 or 1/0.0082644628 = 1 in 121 (Approximately)

Three Hard Eights w/o Loss: (1/11)^3 = 0.0007513148 or 1/0.0007513148 = 1 in 1331 (Approximately)

Four Hard Eights w/o Loss: (1/11)^4 = 0.00006830134 or 1/0.00006830134 = 1 in 14,641 (Approximately)

You could also look at House Edge per roll, but what I wrote above assumes you are going to leave the bet up until it either wins or loses.

3.) You're welcome, nothing tough about it.

4.) With those other bets in comparison, you should be more concerned with either House Edge per Roll or, I would suggest, House Edge per bet resolved. The Fire Bet is always terrible even compared to Hardway bets, but the Small/Tall/All might have a lower house edge depending on how it pays v. how the Hard Eight pays. This can differ from casino to casino.

5.) If you're looking to make a big score and that is your primary concern, then the lowest House Edge and Expected Loss mechanism with which to do that would be to pick one of the lowest House Edge bets on the Table (Pass/Don't Pass with or without Odds...though the Odds will change your bet structure) and to press your bets after wins. You could even do a full Reverse Martingale and you'll expect to lose less money in the long run, though you will still inevitably lose given enough trials.

The reason I asked, is not trying to make a "Big Score" because experience shows that doesn't happen often, but if your going to gamble -- just curious on the betting option. Your answer confirms what I thought, if I'm reading it correctly, it's a better (positive) percentage bet to Skip the fire bet and go for the 1 dollar Hardway parlay 3x if luck repeats (4x parlay repeater would be extremely lucky), I think that's what your answer stated, if reading it correctly.

Also, a side note of interest, I bet a Three way 7 on the come out roll, the 7 rolled four times in a row and I parlayed the seven three times in a row. After the third seven in a row parlayed, moved the 375 to the horn... Lesson learned!!! What are the percentage chances of four 7's in a row..Thanks again!

Thanks for the compliment, I've seen many Craps questions on here so I can usually put together responses pretty quickly. I should really just categorize the answers I have given and keep a file with all of them to copy/paste, probably just have to change a few words.

My answer does indicate that the Hardway bets have a lower house edge than do the Fire Bets, yes, but Pass/Odds or Don't Pass/Odds have lower house edges than Hardway bets, by far. What's wrong with parlaying (Reverse Martingale, essentially) the Pass Line at a reduced expected loss?

Four sevens is easy, a seven happens 1/6 rolls, so (1/6)^4 = 0.00077160493 or 0.077160493% or 1 in 1,296.

By the way, Hop Bets usually have a worse house edge than Hardway bets.

It depends on how many rolls one sees in a session.Quote:VegasHardwaywhat is the percentage chance of Hard 8 rolling three or four times before a Seven out?

say 100 rolls per hour.

more rolls... better chances

Here is data I have

from doing the math. (In excel, of course)

Easier to get Hard6 or Hard8

just a few more $$$s

actually easier to get a Hard4 run (or Hard10)

than a 6 or 8.

shooters are funny that way too.

Oh, yes

look how many rolls it takes on average and the probabilities

to get a feel how often these events occur.

Hard4 (or Hard10)

2 in a row

avg# of rolls 360

1 / 1/36 + 1/36*1/9

36+324

rolls/prob

100: 0.237192384

200: 0.424062664

300: 0.565154034

400: 0.671681271

500: 0.75211179

600: 0.812838687

median # of rolls

251: 0.500960478

3 in a row

avg# of rolls 3276

1 / 1/36 + 1/36*1/9 + 1/36*(1/9)^2

36+324+2916

rolls/prob

100: 0.027898501

200: 0.057194324

300: 0.085607272

400: 0.11316395

500: 0.139890163

600: 0.16581094

median # of rolls

2273: 0.500043273

4 in a row

avg# of rolls 29,520

rolls/prob,1 in

100: 0.002994492, 333.95

200: 0.006367538, 157.05

300: 0.009729171, 102.78

400: 0.013079432, 76.46

500: 0.016418358, 60.91

600: 0.019745988, 50.64

median # of rolls

20465: 0.500001877

*****

Hard6 (or Hard8)

2 in a row

avg# of rolls 432

1 / 1/36 + 1/36*1/11

36+396

rolls/prob

100: 0.202534195

200: 0.368527045

300: 0.499968412

400: 0.604050202

500: 0.686467323

600: 0.751729284

median # of rolls

301: 0.501134044

3 in a row

avg# of rolls 4788

36+396+4356

rolls/prob,1 in

100: 0.019420271,51.49

200: 0.039716067,25.18

300: 0.059591785,16.78

400: 0.079056121,12.65

500: 0.098117589,10.19

600: 0.116784527,8.56

median # of rolls

3321: 0.500067375

4 in a row

avg# of rolls 52,704

rolls/prob,1 in

100: 0.001716119,582.71

200: 0.003608815,277.10

300: 0.005497922,181.89

400: 0.007383448,135.44

500: 0.009265398,107.93

600: 0.011143781,89.74

median # of rolls

36535: 0.500007633

that makes no difference, in agreement with another and doing the math and simulations.Quote:VegasHardwayAlso, it would be nice to know the percentage difference with the hard 8 turned on and off on the come out roll.

Sally

have fun